Chris is probably referring to me.
The weird thing in my case is that they asked for a copy of an UK police record, which I had not applied for before going for the visa interview. I have an old US DUI/DWI and got the US court record, but the embassy helpline told me that was all I needed if I had a US record, no need to prove I had no UK record ... wrong!
Anyway, at the embassy they stamped my passport 'Visa applied for on xyz date and returned it to me'. I went home and then applied for the the UK record. It arrived about a month later (it was blank). I posted it to the US embassy, BUT on the same day I received a letter from the US embassy asking me to send in my passport to be issued the US visa. So they went ahead issuing my US visa, without seeing my UK record, despite demanding it... very weird. Once I sent in my passport, the turn around was a few days.
So, you might be fine. But, it could also depend upon what the conviction was, how long ago etc...
Good luck.